A constable and the robber sustained bullet injuries during the incident around 9 pm on Thursday night, they said.
Indira Puram SHO Deepak Sharma said a police team had signalled two bike-borne youths to stop for checking at Kanawani village.
Instead of halting, the pillion rider fired at the policemen, injuring constable Vijay, the SHO said.
In retaliatory firing, one of the the youths was injured.
The injured person has been identified as Shivraj, a resident of Amarpura village in Sambhal district.
Taking advantage of darkness, his accomplice managed to escape.
Police seized their sports bike, which was allegedly stolen from Shahdara, Delhi.
A countrymade pistol, live cartridge and looted mobiles were seized from Shivraj.
The constable and the accused were rushed to a nearby hospital for treatment.
Shivraj is wanted in over a dozen criminal cases, the SHO said.